Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	284×	body	80	valid
8.0ms	307×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	4
1	14	4
2	14	4

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 22.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b	(* c0 (sqrt (/ A (* V l))))
6.6b	(/ A (* V l))
16.6b	(sqrt (/ A (* V l)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
6×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative`

Counts

3 → 72

Calls

3 calls:

7.0ms	(* c0 (sqrt (/ A (* V l))))
7.0ms	(/ A (* V l))
4.0ms	(sqrt (/ A (* V l)))

series101.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* c0 (sqrt (/ A (* V l))))
20.0ms	(/ A (* V l))
32.0ms	(sqrt (/ A (* V l)))

simplify64.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	215	345
1	819	320
2	3061	317
3	5001	317

prune213.0ms

Filtered

81 candidates to 61 candidates (75.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	65	16	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	16	82

Merged error: 6.7b

Counts

82 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
1.0b	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
3.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
28×	`times-frac`
27×	`add-exp-log`
26×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
14×	`cbrt-prod`
11×	`pow1`
10×	`associate-l`
9×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`sqrt-div` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-prod-down` `associate-*l/`
2×	`sqrt-pow1` `sqrt-prod` `*-commutative` `div-inv`
1×	`pow1/2` `pow1/3`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt A)
11.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
13.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
8.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt A)
67.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
40.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
52.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify65.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	518	1059
1	2563	904
2	5001	844

prune345.0ms

Filtered

126 candidates to 95 candidates (75.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	124	18	142

Merged error: 4.3b

Counts

142 → 18

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
3.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
56×	`times-frac`
46×	`add-exp-log`
44×	`associate-r`
34×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
22×	`cbrt-prod`
16×	`prod-exp` `cbrt-unprod`
14×	`pow1` `cbrt-undiv` `div-exp` `associate-l`
12×	`unswap-sqr`
6×	`sqrt-div`
4×	`expm1-log1p-u` `frac-times` `sqrt-pow1` `associate-r/` `pow-prod-down` `associate-l/` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow1/2` `sqrt-prod` `*-commutative`

Counts

4 → 154

Calls

4 calls:

14.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
14.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
8.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
8.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
42.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
54.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
51.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify57.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	421	1508
1	2054	1332
2	5001	1206

prune594.0ms

Filtered

166 candidates to 126 candidates (75.9%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	15	16
Picked	0	1	1
Done	0	1	1
Total	166	18	184

Merged error: 4.3b

Counts

184 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
16.6b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
12×	`sqrt-div`
8×	`sqrt-pow1`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `frac-times` `add-cube-cbrt` `-un-lft-identity` `pow1/2` `associate-r/` `pow-prod-down` `associate-*l/` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

8.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
8.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
10.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
8.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
50.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
53.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
50.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify73.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	57	532
1	119	504
2	263	504
3	783	492
4	1666	492
5	3074	492
6	5002	492

prune317.0ms

Filtered

76 candidates to 64 candidates (84.2%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	15	15
Picked	0	1	1
Done	0	2	2
Total	76	18	94

Merged error: 4.3b

Counts

94 → 18

regimes711.0ms

Accuracy

30.8% (9.5b remaining)

Error of 14.3b against oracle of 4.7b and baseline of 18.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	20
1	31	20

end0.0ms

sample913.0ms

Algorithm

intervals

Results

245.0ms	8870×	body	80	valid
229.0ms	9106×	body	80	nan